Cot 0 Degrees
The value of cot 0 degrees is undefined(∞). Cot 0 degrees in radians is written as cot (0° × π/180°), i.e., cot (0π) or cot (0). In this article, we will discuss the methods to find the value of cot 0 degrees with examples.
 Cot 0°: undefined(∞)
 Cot 0° in radians: cot (0π) or cot (0 . . .)
What is the Value of Cot 0 Degrees?
The value of cot 0 degrees is ∞. Cot 0 degrees can also be expressed using the equivalent of the given angle (0 degrees) in radians (0 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 0 degrees = 0° × (π/180°) rad = 0π or 0 . . .
∴ cot 0° = cot(0) = undefined(∞)
Explanation:
For cot 0 degrees, the angle 0° lies on the positive xaxis. Thus, cot 0° value = undefined(∞)
Since the cotangent function is a periodic function, we can represent cot 0° as, cot 0 degrees = cot(0° + n × 180°), n ∈ Z.
⇒ cot 0° = cot 180° = cot 360°, and so on.
Methods to Find Value of Cot 0 Degrees
The value of cot 0° is given as undefined(∞). We can find the value of cot 0 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 0 Degrees Using Unit Circle
To find the value of cot 0 degrees using the unit circle:
 Draw the radius of unit circle, ‘r’, to form 0° angle with the positive xaxis.
 The cot of 0 degrees equals the xcoordinate(1) divided by ycoordinate(0) of the point of intersection (1, 0) of unit circle and r.
Hence the value of cot 0° = x/y = undefined(∞).
Cot 0° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 0 degrees as:
 cos(0°)/sin(0°)
 ± cos 0°/√(1  cos²(0°))
 ± √(1  sin²(0°))/sin 0°
 ± 1/√(sec²(0°)  1)
 ± √(cosec²(0°)  1)
 1/tan 0°
We can use trigonometric identities to represent cot 0° as,
 tan (90°  0°) = tan 90°
 tan (90° + 0°) = tan 90°
 cot (180°  0°) = cot 180°
Note: Since 0° lies on the positive xaxis, the final value of cot 0° will be undefined(∞).
☛ Also Check:
Examples Using Cot 0 Degrees

Example 1: Simplify: 4 (cot 0°/tan 45°)
Solution:
We know cot 0° = ∞ and tan 45° = 1
⇒ 4 (cot 0°/tan 45°) = ∞ 
Example 2: Find the value of cot 0° using cos 0° and sin 0°.
Solution:
We know, cot 0° = cos 0°/sin 0°
= 1/0 = undefined(∞) 
Example 3: Find the value of (cos (0°) cosec (0°) sec (0°))/2. [Hint: Use cot 0° = ∞]
Solution:
Using trigonometry formulas,
(cos (0°) cosec (0°) sec (0°))/2 = cos (0°)/(2 sin (0°) cos (0°))
Using sin 2a formula,
2 sin (0°) cos (0°) = sin (2 × 0°) = sin 0°
⇒ cos (0°) / sin (0°) = cot 0°
⇒ (cos (0°) cosec (0°) sec (0°))/2 = ∞
FAQs on Cot 0 Degrees
What is Cot 0 Degrees?
Cot 0 degrees is the value of cotangent trigonometric function for an angle equal to 0 degrees. The value of cot 0° is not defined or ∞.
What is the Value of Cot 0 Degrees in Terms of Sin 0°?
Using trigonometric identities, we can write cot 0° in terms of sin 0° as, cot(0°) = √(1  sin²(0°))/sin 0° . Here, the value of sin 0° is equal to 0.
How to Find Cot 0° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 0° can be given in terms of other trigonometric functions as:
 cos(0°)/sin(0°)
 ± cos 0°/√(1  cos²(0°))
 ± √(1  sin²(0°))/sin 0°
 ± 1/√(sec²(0°)  1)
 ± √(cosec²(0°)  1)
 1/tan 0°
☛ Also check: trigonometry table
How to Find the Value of Cot 0 Degrees?
The value of cot 0 degrees can be calculated by constructing an angle of 0° with the xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cot 0° is equal to the xcoordinate(1) divided by the ycoordinate (0). ∴ cot 0° = undefined(∞)
What is the Value of Cot 0° in Terms of Sec 0°?
We can represent the cotangent function in terms of the secant function using trig identities, cot 0° can be written as 1/√(sec²(0°)  1). Here, the value of sec 0° is equal to 1.
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